# Consider two consumers, A and B. A and B both want perfect consumption smoothing (c = cf) and both have…

Consider two consumers, A and B. A and B both want perfect consumption smoothing (c = cf) and both have no current wealth. However, the two consumers have different income streams. Person A’s current income, yA, = 100, and future income, yfA, = 121. Person B’s current income, yB, is 120, and future income, yfB, = is 99. The real interest rate is 10%.

(a). Calculate the present value of lifetime resources (PVLR) for consumer A and consumer B, respectively.
(b). Draw consumer A’s budget constraint. How does the budget constraint of consumer A compare to the budget constraint of consumer B? Explain.
(c). Find consumer A’s optimal lifetime consumption plan, (cA, cfA). How does consumer B’s optimal lifetime consumption plan, (cB, cfB), compare to consumer A’s lifetime consumption plan? Explain.
(d). Is consumer A a current saver or a current borrower? Explain. Is consumer B a current saver or a current borrower? Explain.
(e). Draw a graph that illustrates how an increase in the interest rate (above 0.10) will affect the budget constraints of consumer A and consumer B. How does the budget constraint of consumer A compare to the budget constraint of consumer B?

2. (15 points) Fred’s Frisbees is trying to determine how many Frisbee pressing machines to buy for its new factory. The real price of a new pressing machine is 7500 Frisbees. The depreciation rate on these Frisbee presses is equal to 10% per year. The expected future marginal product of these fabricating machines is given by the expression 3350 – 20K, measured in Frisbees. The real interest rate is 8% (.08).

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(a) What is the user cost of capital?
(b) What is the profit-maximizing number of Frisbee presses for Fred’s to purchase for its new factory?
(c) Before purchasing the machines Fred’s finds that it will be subject to a new tax of 32.5 percent on all of its revenue. Now what is the profit maximizing number of machines for Fred’s to purchase? (Round down to the nearest whole number.)

3. (25 points)
Desired consumption for an economy is given by the equation
Cd = 1000 + .6Y – 4000r.
Government purchases are given by G = 1500.

(a) Write an expression relating desired saving, Sd, to Y and r.
(b) Suppose that the full-employment level of output is 10,000. Graph the relationship between desired saving, Sd, and the real interest rate r. (Your graph should include properly labeled axes and an indication of the scale on each axis.)
(c) If desired investment for the economy is given by the equation
Id = 2000 – 6000r,
calculate the equilibrium real interest rate for the economy.
(d) Using the equilibrium real interest rate that you calculated in part (c), calculate the equilibrium level of saving, investment, and consumption in the economy.
Does Y = C + I + G in equilibrium?
(e) Add the relationship between desired investment and the real interest rate to your graph in part (b), and show the equilibrium values of r, Sd and Id from parts (c) and (d)

4. (20 points) Analyze the effects of each of the following on national saving, investment, and the real interest rate. Explain your reasoning and illustrate it with an appropriate diagram.

(a) Consumer confidence falls, so consumers decide to consume less and save more at every level of the real interest rate.
(b) The government announces a larger, one-time bones payment to veterans returning from a war. The bonus will be financed by additional taxes levied on the general population over the next five years.
(c) The government introduces an investment tax credit (offset by other types of taxes, so total tax collections remain unchanged)
(d) A new technology breakthrough increases the future marginal product of capital and expected future income.